JP2008134097A - Sensor device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a sensor device capable of securing sufficient sensitivity, even when using a sensor element having a small variation of an electrical quantity taken out corresponding to a change of a physical quantity or a chemical quantity. <P>SOLUTION: A current voltage conversion part 5 has a plurality of capacitors C1-C3 charged by a current signal from a current conversion part 3 respectively, and a plurality of switch elements S1-S12 as connection switching means for switching a connection relation between the plurality of capacitors C1-C3. Each switch element S1-S12, whose on-off state is controlled by each control signal ϕ1-ϕ6 from a control part, connects the plurality of capacitors C1-C3 in parallel so that each capacitor C1-C3 is charged by a current signal when inputting the current signal, and connects the plurality of capacitors C1-C3 in series so that the sum of both end voltages of the plurality of capacitors C1-C3 is outputted when outputting a voltage signal. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a sensor device that detects a physical quantity or a chemical quantity and outputs a voltage signal.

  Conventionally, as shown in FIG. 11, a sensor device including a sensor unit 4 having a sensor element 2 that converts a physical quantity or a chemical quantity into an electric quantity and a detection circuit 30 that detects an output of the sensor unit 4 is known. (See, for example, Patent Document 1).

  The detection circuit 30 in FIG. 11 has a storage capacitor C10, and detects the sensor output by discharging the charge of the storage capacitor C10 in accordance with the output of the sensor unit 4. The detection circuit 30 includes a sense amplifier circuit 31 that detects and amplifies a change in the output of the sensor unit 4, a current-voltage conversion circuit 32 that converts an output current of the sense amplifier circuit 31 into a voltage, and an output of the current-voltage conversion circuit 32. Is provided with a discharge circuit 33 for discharging the electric charge of the storage capacitor C10 and an output circuit 34 for outputting the voltage across the storage capacitor C10.

Here, in the example of FIG. 11, the current-voltage conversion circuit 32 includes a current mirror circuit (PMOS transistors MP1 and MP2), and thus the sense amplifier circuit 31 and the storage capacitor C10 are separated, so that The amplifier circuit 31 is not affected by the voltage across the storage capacitor C10, and the circuit linearity is improved. Therefore, it is possible to realize a sensor device with relatively high sensitivity.
Japanese Patent Laying-Open No. 2003-250088 (page 6, FIG. 1)

  By the way, as the sensor element 2 in FIG. 11, it is conceivable to use a minute sensor element such as a sensor element using MEMS (Micro Electro Mechanical Systems) technology which has been proposed in recent years. However, in this type of sensor element 2, the amount of change in the amount of electricity taken out in accordance with the change in physical quantity or chemical quantity is also relatively small. Therefore, when this type of sensor element 2 is used in the invention described in Patent Document 1, the amount of change in the voltage across the storage capacitor C10 is also small, and it is difficult to ensure sufficient sensitivity.

  The present invention has been made in view of the above reasons, and even when a sensor element having a small amount of change in electrical quantity taken out in accordance with a change in physical quantity or chemical quantity is used, sufficient sensitivity can be ensured. An object of the present invention is to provide a sensor device that can be used.

  According to the first aspect of the present invention, a sensor unit having a sensor element that converts a physical quantity or a chemical quantity into an electric quantity, a current converter that converts the output of the sensor part into a current signal, and a current signal from the current converter are input. A current-voltage converter that outputs a voltage signal as a current-voltage converter, each of which is charged with a current signal from the current converter, and each capacitor is input with a current signal when the current signal is input. Connection switching means for connecting the plurality of capacitors in series so that the plurality of capacitors are connected in parallel so as to be charged, and the sum of voltages across the plurality of capacitors is output when a voltage signal is output. It is characterized by that.

  According to this configuration, the current-voltage conversion unit connects the plurality of capacitors in parallel by the connection switching unit so that each capacitor is charged with the current signal when the current signal is input, and the plurality of capacitors when the voltage signal is output. Since a plurality of capacitors are connected in series by the connection switching means so as to output the sum of the voltages at both ends, the current signal from the current converter is converted into a voltage signal and amplified with an amplification factor according to the number of capacitors. Is output. Therefore, even when a sensor element with a small change in the amount of electricity extracted in accordance with a change in physical quantity or chemical quantity is used, the voltage signal output from the sensor device changes relatively greatly, ensuring sufficient sensitivity. can do.

  According to a second aspect of the present invention, in the first aspect of the present invention, the switch is inserted between the sensor unit and the current conversion unit and separates the sensor unit from the current conversion unit in the off state, and the switch is off. In a state, a circuit offset register that holds a voltage signal output from the current-voltage conversion unit that receives a current signal from the current conversion unit as a circuit offset value, and from the current conversion unit in a state in which the switch is on A sensor signal register that holds, as a sensor signal value, an output voltage signal output from the current-voltage conversion unit that has input a current signal, and a circuit offset value that is held in a circuit offset register from the sensor signal value held in the sensor signal register And an arithmetic unit that outputs a value obtained by subtracting.

  According to this configuration, the computing unit outputs a value obtained by subtracting the circuit offset value from the sensor signal value. Therefore, in the output of the computing unit, the electric charge possessed by the components of the current conversion unit and the current-voltage conversion unit is included. A value obtained by removing the resulting circuit offset component, that is, a sensor detection component corresponding only to the output of the sensor unit can be extracted as a detection result, and detection accuracy is improved.

  In the present invention, the current-voltage conversion unit includes a plurality of capacitors that are charged by current signals from the current conversion units, and a plurality of capacitors that are connected in parallel so that each capacitor is charged by the current signal when the current signal is input. Since it has connection switching means for connecting a plurality of capacitors in series so as to output the sum of voltages across the plurality of capacitors when connecting and outputting a voltage signal, it is taken out in accordance with a change in physical quantity or chemical quantity Even when a sensor element with a small amount of change in the amount of electricity is used, the output voltage signal changes relatively greatly, and there is an advantage that sufficient sensitivity can be secured.

(Embodiment 1)
As shown in FIG. 1, the sensor device 1 of the present embodiment includes a sensor unit 4 having a sensor element 2 that converts a physical quantity or a chemical quantity into an electric quantity, and current conversion that converts an output of the sensor part 4 into a current signal. Unit 3, current-voltage conversion unit 5 that outputs a voltage signal with the current signal from current conversion unit 3 as an input, and output unit 6 that outputs the output of current-voltage conversion unit 5 to a subsequent circuit (for example, an arithmetic circuit) Is provided.

  Here, as an example of the sensor element 2, there is one that changes the amount of electricity in accordance with a temperature rise caused by receiving infrared rays. Since this type of sensor element 2 can be manufactured using MEMS (Micro Electro Mechanical Systems) technology, a sensor array can be configured by arranging a large number of sensor elements 2 on a single substrate. It is. The sensor unit 4 according to the present embodiment outputs a voltage signal corresponding to a change in the amount of electricity in the sensor element 2 to the current conversion unit 3. When the sensor unit 4 includes a plurality of sensor elements 2, a current conversion unit 3 that outputs a current signal corresponding to the output of the sensor element 2 is provided for each sensor element 2 as shown in FIG. As shown in FIG. 2B, a current conversion unit 3 that outputs a difference (A−B) of outputs of a plurality (here, two) of sensor elements 2 as a current signal may be used. .

  By the way, the current-voltage conversion part 5 of this embodiment is a connection switching means for switching the connection relationship between a plurality of capacitors C1 to C3 and a plurality (three in the illustrated example) of capacitors C1 to C3 as shown in FIG. It has a plurality of switch elements S1 to S12. Specifically, the current-voltage conversion unit 5 includes a signal line 7 connected to the current conversion unit 3 via the first switch element S1.

  The first capacitor C1 has one end connected to the signal line 7 via the second switch element S2 and the other end to a reference potential point (for example, a housing ground potential point) of the circuit maintained at the reference potential Vs. It is connected. The second capacitor C2 has one end connected to the signal line 7 via the third switch element S3 and the other end connected to the reference potential point via the fourth switch element S4. The third capacitor C3 has one end connected to the signal line 7 via the fifth switch element S5 and the other end connected to the reference potential point via the sixth switch element S6. With this configuration, the first to third capacitors C1 to C3 are connected in parallel between the signal line 7 and the reference potential point of the reference potential Vs while the second to sixth switch elements S2 to S6 are all turned on. Will be connected to.

  On the other hand, one end of the first capacitor C1 and the other end of the second capacitor C2 are connected via a seventh switch element S7, and one end of the second capacitor C2 and the other end of the third capacitor C3 are connected. It is connected via an eighth switch element S8. As a result, the second, third, fifth, and sixth switch elements S2, S3, S5, and S6 are off, and the fourth, seventh, and eighth switch elements S4, S7, and S8 are on. Thus, the first to third capacitors C1 to C3 are connected in series between the signal line 7 and the reference potential point of the reference potential Vs. Here, the signal line 7 is connected to the input terminal of the buffer 8 constituting the output unit 6 via a ninth switch element.

  One end of the first capacitor C1 is connected to the reference potential point via the tenth switch element S10, and one end of the second capacitor C2 is connected to the reference potential point via the eleventh switch element S11. One end of the third capacitor C3 is connected to the reference potential point via the twelfth switch element S12. The tenth to twelfth switch elements S10 to S12 are reset switch elements for the capacitors C1 to C3, and the fifth, sixth, and tenth to twelfth switch elements S5, S6, S10 to S12. When is turned on, both ends of the capacitors C1 to C3 are connected to the reference potential point of the reference potential Vs.

  Here, the operation of the current-voltage conversion unit 5 configured as described above includes a first step ST1 for resetting the capacitors C1 to C3, and a second step for inputting (sampling) a current signal from the current conversion unit 3. The process is divided into four steps, step ST2, a third step ST3 for amplifying the voltage signal according to the current signal, and a fourth step ST4 for outputting the amplified voltage signal to the output unit 6. For each ST4, the on / off states of the switch elements S1 to S12 are controlled by control signals φ1 to φ6 from a control unit (not shown). Here, the first to third switch elements S1 to S3 are turned on and off by the same control signal φ1, the fourth switch element S4 is turned on and off by the control signal φ3, and the fifth and sixth switch elements S5 and S6 are The seventh and eighth switch elements S7, S8 are turned on / off by the same control signal φ2, the ninth switch element S9 is turned on / off by the control signal φ6, and the tenth to twelfth switches are turned on / off by the same control signal φ5. The switch elements S10 to S12 are turned on / off by the same control signal φ4.

  FIG. 3 shows on / off control states of the switch elements S1 to S12 for each of the steps ST1 to ST4. In FIG. 3, control signals φ1 to φ6 are shown, and each switch element S1 to S12 is turned on when the corresponding control signal φ1 to φ6 is at a high level (H), and when it is at a low level (L). Turn off.

  Below, operation | movement of the sensor apparatus 1 of this embodiment is demonstrated with reference to FIGS.

  In the first step ST1, the fifth, sixth, tenth to twelfth switch elements S5, S6, S10 among the plurality of switch elements S1 to S12 as shown in FIG. Only S12 is turned on. In this state, both ends of the first to third capacitors C1 to C3 are connected to the reference potential point of the reference potential Vs, and the charges accumulated in the capacitors C1 to C3 are discharged, so that the capacitors C1 to C3 are discharged. Reset. At this time, the signal line 7 is not connected to either the current conversion unit 3 or the output unit 6. In the first step ST1 for resetting the capacitors C1 to C3, instead of a configuration in which both ends of the capacitors C1 to C3 are connected to the reference potential point, a configuration in which both ends of the capacitors C1 to C3 are short-circuited is adopted. May be.

  Next, in the second step ST2, only the first to sixth switch elements S1 to S6 among the plurality of switch elements S1 to S12 are turned on by the control signals φ1, φ3, and φ5 as shown in FIG. . In this state, the first to third capacitors C1 to C3 are connected in parallel between the signal line 7 and the reference potential point of the reference potential Vs, and the signal line 7 is connected to the output of the current conversion unit 3. . Therefore, each of the capacitors C1 to C3 is charged by the current signal from the current converter 3. That is, charges corresponding to the output of the current converter 3 are accumulated in the capacitors C1 to C3.

  In the next third step ST3, only the seventh and eighth switch elements S7 and S8 are turned on among the plurality of switch elements S1 to S12 as shown in FIG. 6 by the control signal φ2. In this state, the first to third capacitors C1 to C3 are connected in series. Between both ends of the series circuit (that is, the terminal on the reference potential Vs side of the first capacitor C1 and the third capacitor C3). The sum of the voltages charged in the first to third capacitors C1 to C3 appears between the fourth switch element S4 and the terminal on the fourth switch element S4 side. That is, a potential obtained by summing the voltages across the first to third capacitors C1 to C3 is generated at the terminal on the fourth switch element S4 side of the third capacitor C3. At this time, the signal line 7 is not connected to either the current conversion unit 3 or the output unit 6.

  In the next fourth step ST4, only the fourth to seventh switch elements S4, S7 to S9 among the plurality of switch elements S1 to S12 as shown in FIG. 7 by the control signals φ2, φ3, and φ6 are shown. Is turned on. Here, the control signal φ2 is maintained at the high level (H) when the third step ST3 is shifted to the fourth step ST4, and the seventh and eighth switch elements S7 and S8 are continuously turned on. . In this state, the series circuit including the first to third capacitors C1 to C3 is connected between the signal line 7 and the reference potential point of the reference potential Vs, and the signal line 7 is connected to the input of the output unit 6. The Therefore, a voltage obtained by summing the voltages across the first to third capacitors C1 to C3 is input to the output unit 6 as a voltage signal. The output unit 6 takes out the input voltage to a subsequent circuit (for example, an arithmetic circuit) by the buffer 8.

  As described above, by sequentially executing the four steps ST1 to ST4, the current-voltage converter 5 functions as a charge pump, resets the first to third capacitors C1 to C3, inputs the current signal, and the voltage signal. Amplification and voltage signal output in this order. Here, the potential V1 (see FIG. 1) of the terminal on the fourth switch element S4 side in the third capacitor C3 and the output potential V2 (see FIG. 1) of the output unit 6 change for each of steps ST1 to ST4. For example, as shown in FIG. 8, both potentials V1 and V2 are both at the reference potential Vs in the first step ST1, the potential V1 becomes the charging potential Vc3 of the capacitor C3 in the second step ST2, and the potential V1 in the third step ST3. Becomes the potential Vall obtained by summing the voltages across all the capacitors C1 to C3. In the fourth step ST4, both the potentials V1 and V2 become the potential Vall.

  The sensor device 1 of the present embodiment intermittently amplifies the current signal output from the current converter 3 and outputs it as a voltage signal (voltage value) by periodically repeating the above four steps ST1 to ST4. be able to. According to this configuration, since the current-voltage converter 5 functions as a charge pump and amplifies the current signal from the current converter 3 and outputs it as a voltage signal, the change in the current signal output from the current converter 3 Even if the amount is very small, a voltage signal having a relatively large change amount can be extracted from the output unit 6. As a result, there is an advantage that sufficient sensitivity can be ensured even when the sensor element 2 having a small amount of change in the amount of electricity extracted in accordance with a change in physical quantity or chemical quantity is used.

  In the embodiment described above, an example in which the number of capacitors C1 to C3 is three has been described. However, the number of capacitors provided in the current-voltage conversion unit 5 is not limited to three and may be plural. For example, when four capacitors are provided, one end of the fourth capacitor is connected in series between the second capacitor C2 and the third capacitor C3 in the third step ST3. Is connected to the other end of the third capacitor C3 through a switch element that is controlled to be turned on / off by the control signal φ2, and one end of the second capacitor C2 is connected to the other end of the fourth capacitor through the eighth switch element S8. Connect to In this case, the other connection relationship of the fourth capacitor is the same as that of the second capacitor C2, and one end of the fourth switch element is connected to the signal line 7 via a switch element that is ON / OFF controlled by the control signal φ1. At the same time, it is connected to the reference potential point of the reference potential Vs through a switch element that is ON / OFF controlled by the control signal φ4. Further, the other end of the fourth switch element is connected to the reference potential point via a switch element that is ON / OFF controlled by a control signal φ5.

(Embodiment 2)
As shown in FIG. 9, the sensor device 1 of the present embodiment has a switch SW added between the sensor unit 4 and the current conversion unit 3, and an arithmetic circuit 9 is added after the output unit 6. This is different from the sensor device 1 of the first embodiment. The switch SW separates the sensor unit 4 from the current conversion unit 3 when it is off, and is on / off controlled by a control signal φ7 (see FIG. 10) from the control unit. Other configurations and functions are the same as those of the first embodiment.

  The arithmetic circuit 9 has an AD converter 10 for AD (analog-digital) conversion of an analog voltage signal (voltage value) output from the output unit 6, and the output destination is the first output 11 a at the subsequent stage of the AD converter 10. And a selection circuit 11 that selectively selects from the second output 11b. A circuit offset register 12 that holds the output of the AD converter 10 as a circuit offset value is connected to the first output 11a of the selection circuit 11, and the output of the AD converter 10 is connected to the sensor signal as the second output 11b of the selection circuit 11. A sensor signal register 13 that holds values is connected. The circuit offset register 12 and the sensor signal register 13 are connected to an arithmetic unit 14 that subtracts a value (circuit offset value) in the circuit offset register 12 from a value (sensor signal value) in the sensor signal register 13 and outputs the result. The output of the computing unit 14 is held in the output register 15 as a detection result.

  The operation of the current-voltage converter 5 is divided into first to fourth steps ST1 to ST4 as in the first embodiment, and the on / off states of the switch elements S1 to S12 are not shown for each step ST1 to ST4. It is controlled by control signals φ1 to φ6 from the unit. On the other hand, the operation of the sensor device 1 as a whole is set after the circuit offset information collection period T1 composed of the four steps ST1 to ST4 and the circuit offset information collection period T1, and the signal information composed of the four steps ST1 to ST4. It is classified into two periods, the collection period T2. That is, the entire operation of the sensor device 1 is divided into eight steps, that is, four steps ST1 to ST4 in the circuit offset information collection period T1, and four steps ST1 to ST4 in the signal information collection period T2. Each time these eight steps are performed, the detection result is output to the output register 15.

  FIG. 10 shows on / off control states of the switch elements S1 to S12 and the switch SW for each of the steps ST1 to ST4. In FIG. 10, control signals φ1 to φ7 are shown. The switch elements S1 to S12 and the switch SW are turned on when the corresponding control signals φ1 to φ7 are at a high level (H), and are at a low level (L). Sometimes off. The switch SW is turned on by the control signal φ7 only in the second step ST2 in the signal information collection period T2, and is in the off state in other steps. Further, the selection circuit 11 selects the first output 11a in the fourth step ST4 of the circuit offset information collection period T1, and selects the second output 11b in the fourth step ST4 of the signal information collection period T2. Be controlled.

  By the way, if a voltage signal corresponding only to the output of the sensor unit 4 can be output, the detection accuracy as the sensor device 1 increases, but actually, the components of the current converter 3 and the current-voltage converter 5 are charged. When this charge is accumulated in the capacitors C1 to C3 of the current-voltage conversion unit 5, the charge may be superimposed on the output component of the sensor unit 4 and output.

  Specifically, if a transistor is used for the switch elements S1 to S12 of the current-voltage conversion unit 5, noise (1 / f noise, thermal noise, etc.) generated in the transistor is used as the charge as the capacitor C1 of the current-voltage conversion unit 5. May accumulate in ~ C3. Also, processing variations due to semiconductor process mismatch may occur during device manufacture. For example, when the gate width of a MOS transistor is different from a design value, the amount of current flowing changes. As a result, an error constantly occurs between the designed circuit output and the actual circuit output, and this error is superimposed on the output component of the sensor unit 4. That is, assuming that a component corresponding only to the output of the sensor unit 4 is a sensor detection component and a component corresponding to an electric charge of a circuit component is a circuit offset component, a voltage in which the circuit offset component is superimposed on the sensor detection component When the signal is output from the output unit 6, the detection accuracy of the sensor device 1 is reduced by the amount of the circuit offset component.

  On the other hand, the sensor device 1 of the present embodiment can output the sensor detection component from which the influence of the circuit offset component described above is removed by subtracting the circuit offset value from the sensor signal value by the computing unit 14 and outputting the result. It is what.

  Below, operation | movement of the sensor apparatus 1 of this embodiment is demonstrated with reference to FIG.

  In the circuit offset information collection period T1, the current-voltage conversion unit 5 operates in a state where the switch SW is always off and the sensor unit 4 is separated from the current conversion unit 3. The current-voltage converter 5 operates in the same manner as in the first embodiment in each of steps ST1 to ST4, whereby a voltage signal corresponding to the current signal from the current converter 3 is output via the output unit 6 in the fourth step ST4. Is output to the arithmetic circuit 9. At this time, since the selection circuit 11 selects the first output 11a, the output from the output unit 6 is held as a circuit offset value in the circuit offset register 12 after AD conversion.

  Here, the value held in the circuit offset register 12 as the circuit offset value corresponds to a circuit offset component caused by the electric charge possessed by the components of the current converter 3 and the current-voltage converter 5.

  On the other hand, in the signal information collection period T2, the switch SW is turned on to connect the sensor unit 4 to the current conversion unit 3 in the second step ST2 in which the current-voltage conversion unit 5 inputs the current signal from the current conversion unit 3. In this state, the current / voltage converter 5 operates. The current-voltage conversion unit 5 operates in the same manner as in the first embodiment in each of steps ST1 to ST4, whereby a voltage signal corresponding to the current signal from the current conversion unit 3 is output via the output unit 6 in the fourth step ST4. Is output to the arithmetic circuit 9. At this time, since the selection circuit 11 selects the second output 11b, the output from the output unit 6 is held as a sensor signal value in the sensor signal register 13 after AD conversion.

  Here, the value held in the sensor signal register 13 as the sensor signal value is a charge that the components of the current conversion unit 3 and the current-voltage conversion unit 5 have as a sensor detection component corresponding only to the output of the sensor unit 4. This corresponds to a value in which the circuit offset component due to the above is superimposed. Thereafter, the arithmetic unit 14 outputs a value obtained by subtracting the circuit offset value from the sensor signal value to the output register 15 as a detection result, and causes the output register 15 to hold it.

  As a result, since the detection result obtained by removing the circuit offset component from the value obtained by superimposing the circuit offset component on the sensor detection component is held in the output register 15, the circuit offset is obtained by extracting the detection result. The sensor detection component from which the influence of the component is removed can be taken out. Therefore, a voltage signal corresponding only to the output of the sensor unit 4 can be taken out as a detection result, and there is an advantage that detection accuracy is improved.

It is a schematic circuit diagram which shows the structure of Embodiment 1 of this invention. (A) is a schematic circuit diagram which shows the structure of a sensor part and an electric current conversion part same as the above, (b) is a schematic circuit diagram which shows the other structure of a sensor part and an electric current conversion part same as the above. It is operation | movement explanatory drawing same as the above. It is operation | movement explanatory drawing of the 1st step same as the above. It is operation | movement explanatory drawing of the 2nd step same as the above. It is operation | movement explanatory drawing of a 3rd step same as the above. It is operation | movement explanatory drawing of a 4th step same as the above. It is operation | movement explanatory drawing same as the above. It is a schematic circuit diagram which shows the structure of Embodiment 2 of this invention. It is operation | movement explanatory drawing same as the above. It is a circuit diagram which shows a prior art example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Sensor apparatus 2 Sensor element 3 Current conversion part 4 Sensor part 5 Current voltage conversion part 12 Circuit offset register 13 Sensor signal register 14 Calculator C1-C3 Capacitor S1-S12 Switch element (connection switching means)
SW switch

Claims (2)

  A sensor unit having a sensor element that converts a physical quantity or a chemical quantity into an electric quantity, a current conversion part that converts the output of the sensor part into a current signal, and a current that outputs a voltage signal with the current signal from the current conversion part as an input A voltage conversion unit, and each of the current voltage conversion unit is charged with a current signal from the current conversion unit, and the plurality of capacitors are charged with the current signal when the current signal is input. And a connection switching means for connecting the plurality of capacitors in series so as to output a sum of voltages across the plurality of capacitors when a voltage signal is output. . A switch that is inserted between the sensor unit and the current conversion unit and separates the sensor unit from the current conversion unit in an OFF state, and a current signal from the current conversion unit is input in the OFF state. A circuit offset register that holds a voltage signal output from the current-voltage converter as a circuit offset value, and an output output from the current-voltage converter that receives a current signal from the current converter while the switch is on. A sensor signal register that holds the voltage signal as a sensor signal value, and a calculator that outputs a value obtained by subtracting the circuit offset value held in the circuit offset register from the sensor signal value held in the sensor signal register. The sensor device according to claim 1, wherein:

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